A Wavelet Based Approach for Fast
Detection of Internal Fault in Power Transformers
The power transformer is one of the most expensive elements of power system and its protecti on is an esse ntial part of the overall system protect ion strategy. The differe ntial protect ion provides the best protect ion for power tran sformer. Its operati on prin ciple is based on this point that the differe ntial curre nt duri ng an internal fault is higher tha n no rmal con diti on. But, a large tran sie nt curre nt (i nrush curre nt> can cause mal-operati on of differe ntial relays. Then, studies for the improveme nt of the tran sformer protecti on have focused on discrim in ati on betwee n in ternal short circuit faults and in rush curre nts in tran sformers. The magn etiz ing in rush curre nt has a large sec ond order harm onic comp onent in comparis on to in ternal faults. Therefore , some tran sformer protecti on systems are desig ned to halt operat ing duri ng the in rush curre nt by sensing this large sec ond order harm onic. The sec ond harm onic comp onent in the magn etiz ing in rush curre nts tend to be relatively small in moder n large power tran sformers because of improveme nts in the power tran sformer core materials. Also , it has bee n see n that the fault curre nt can contain higher sec ond order harm onics tha n the in rush curre nt due to non li near fault resista nee, CT saturati on .the distributed capacitance in the transmission line, which transformer is connected to, or due to the use of extra high voltage underground cables. Various methods have been suggested for overcoming this protection system mal-operation. b5E2RGbCAP
This paper prese nts a wavelet based method for discrim in ati on among in rush curre nt, internal short circuit ,exter nal short circuit and en ergiz ing and it is not affected by CT saturati on and it is able to detect in ternal faults while tran sformer en ergizati on. Un like Artificial Neural Network and Fuzzy logic based algorithms. This approach is not system dependent. The operating time of the scheme is less tha n 10ms. The Daubechies mother wavelet is used with a sample rate of 5 kH z. Then , the differential currents of the three phases are decomposed into two details and only the second level will be considered by using db5 mother wavelet. p1EanqFDPw Discrete Wavelet Tran sform
The wavelet transform is a powerful tool to extract information from the non-stationary signals
simultaneously in both time and frequency domains. The ability of the wavelet transform to focus on short time intervals for high-frequency components and long intervals for low- frequency components improves the analysis of transient phenomena signals. Various wavelet functions ,such as Symlet,Morlert and Daubechies are used to analyze different power system phenomena. The mother wavelet must be selected performed based on its application and the features of sig nal .which should be processed. In this paper, Daubechies wavelet is used. There are three types of wavelet transform. Which are Continuous Wavelet Transform(CWT>. Discrete Wavelet Transform(DWT> and Wavelet Packet Transform(WPT>. DWT is derived from CWT. Assume that x(t> is a tome variable sig nal, then the CWT is determi ned by (1>: DXDiTa9E3d
(1>
Where,「and _i are translating and scaling parameters,
respectively. Also , 一 is the wavelet function and 一 is the complex conjugate of 一 . Wavelet function must
satisfy(2>
and should have limited energy: RTCrpUDGiT
X
I (2>
Then ,the discretized mother wavelet is as follows : 5PCzVD7HxA
Where, >1 and I >0 and they are fixed real values. Also ,」and are positive integers.
DWT is expressed by (4>:jLBHrnAILg
(4>
Where, _l is the complex conjugate of 丨 .In (4>, the mother wavelet is dilated and translated
and).xHAQX74J0X (5>
discretely by selecting
一I
and __________ I
DWT can be easily and quickly implemented by complementary low pass and high-pass filters. LDAYtRyKfE
Proposed Algorithm
In the proposed algorithm, the DWT is applied to the differential currents of three phases. The Daubechies
Db-5 type wavelet is used as the mother wavelet and the sig nals are decomposed up to the sec on d-level. The n , the spectral en ergy and sta ndard deviati on of the decomposed signals in the level proposed method consists of two steps。detection and discrim in ati on. Zzz6ZB2Ltk
Disturba nee Detecti on
Under normal conditions and external faults, the differential currents have smaller values than internal
faults. However in some operati ng con diti ons, the exter nal faults can result in high differential currents due to ratio mismatch of CTs or tap changes of power transformer. Then ,these conditions may cause mal-operation of the relay. Therefore ,a threshold current is used in order to prevent malfunctions caused by non-faulty currents. If one of differential currents exceeds this threshold value, it will be identified as a fault. The threshold value id defined, as
are
calculated.
The
follows:」dvzfvkwMIl
(6>
Where I and I are the sec on dary and primary CT curre nts, respectively, and is the slope of the differe
ntial relay characteristic. If ________________________________________ , the n the detect ion algorithm
defines it as an internal fault. rqyn^ZNXi
Disturbance Discrimination
In order to classify disturba nces, the differe ntial curre nts are decomposed up to the sec ond level,
using Daubechies Db5 type wavelet with data window less than the half of the power freque ncy cycle. A sampli ng rate of 5 kHz, is con sidered for the algorithm(i.e .. 100 samples per power freque ncy cycle based on 50 Hz>. Then, the en ergy and sta ndard deviati on in the sec ond detail are calculated for each differe ntial curre nt. It is see n that the spectral en ergy as well as the sta ndard deviatio n in 」level tends to have high values duri ng in rush curre nts. The n , a discrim in ati on in dex ( 一 >ca n be calculated by multipl ying the spectral en ergy by sta ndard
deviati on in the sec ond detail for each differe ntial curre nt, as follows: EmxvxOtOco
I
(7>
Where, STD is the standard deviation in 二 detail and E is its spectral energy.
can be determined using the following equation: SixE2yXPq5
The STD
Where, 一 is n-th coefficient from detail 2. I is its mean value and M is the total number of existed
coefficients. Then , the spectral energy of the wavelet signal in the 一 level is calculated by (9>: 6ewMyirQFL
也]
(9>
The n , the n discrim in ati on in dex ( — > will be compared with a threshold value (
The relay will be activated, if any one of the three-phase differential currents exceeds this threshold value( 一 >.kavU42VRUs
— >.
译文:
一个基于小波变换对电力变压器内部故障快速检测的方法
电力变压器是电力系统中最重要的部分之一,并且其保护是整个系统的保护策略中重 要组成部分。差动保护为电力变压器提供最好的保护。其工作原理是差动电流在内部故障 时的值高于正常状态,但是一个大的瞬态电流
(涌流>会导致差动继电器的误动。对变压器
保护的改进的研究集中在变压器内部短路电流和冲击电流的识别。与内部故障相比,励磁 涌流有大量二阶谐波分量。因此,一些变压器保护系统会在检测到大量的二阶谐波分量判 断涌流而中断变压器工作。现代大型电力变压器由于电力变压器的核心材料的改进使励磁 涌流的二次谐波分量变得相对较小。同时
因有非线性故障电阻、
,故障电流会比涌流包含更高的二阶谐波分量,原
CT饱和、连接变压器输电线路的分布电容、或因使用过高压地下电
缆。已经提出了各种方法来克服这一保护系统的误动。
y6v3ALoS89
本文提出了一种在判别涌流、内部短路、外部短路与励磁的基于小波变换的方法,它 不受CT饱和的影响并且当变压器励磁时它可以探测到内部故障。不同与人工神经网络和模 糊逻辑基础算法。该方法不依赖系统。该方案的响应时间少于
10毫秒。基小波采样频率为
db5基小波
5
kHz。那么,三项电的差动电流分解成两个步骤,并且只有第二阶段会考虑使用
。M2ub6vSTnP 离散小波变换。
小波变换在同时在时域和频域提取非平稳信号的信息是一个功能强大的工具。小波变 换能够在高频时时频窗变窄和低频时变宽来提高对瞬变电流的分析。有多种小波变换,例 如Symlet、Morlert和
Daubechies小波变换用于分析不同的电力系统现象。基小波的选择必 须依赖于他的应用及信号的特点。
在本文中,使 Daubechies小波变换有三种小波变换方式
。连续小波变换(CWT>、离散小波变换(DWT>和小波包变换(WPT>,DWT来源于CWT。 假设x(t>是一个时变信号,那么 CWT就由(1>式决定:0YujCfmUCw
其中, 和 分别是转换和尺度参数。同时, 数。小波函数必须满足(2>并且应该有限能量:
1-1是小波函数和—是21共轭复
(2>
那么,离散基小波如下:
(3>
其中,叵>1和耳>0并且它们是固定实数。另外, 如下:
和 是正整数。DWT由<4)表示
其中,厂 是|:“]共轭复数。在<4)中,基小波通过选定 化:
一工.1 and 一乂-
(5>
和 来表述和转
DWT可以由互补的低通和高通滤波器方便而快速地实现。
处理算法:
在处理算法中, DWT用于三相电的差分电流。
Daubechies的Db-
5类型的小波为作为基小波,信号分解到第二层。然后分解信号的光谱能量和标准偏差在
1
—水平进行了计算分析。该方法有两个步骤。检测和鉴别。 干扰检测:
eUts8ZQVRd
在正常的条件和外部故障时的差分电流比在内部故障时要小。但是 ,在某些条件下,由
于CT比率不匹配或电力变压器的振动变化会导致较高的差分电流。然后,这些状况可能引 起继电器的误动。因此,一个阈值电流用于防止非故障电流引起的误动。如果差分电流超 过阈值,它将被认定为发生了故障。阈值定义如下:
sQsAEJkW5T
(6>
其中, 丨和 尸|分别是CT的次级和初级电流, .=丨,然后检测算法将它定义成为一个内部错误。 干扰识别:
是差动继电器特征斜率。如果
GMslasNXkA
为了对干扰进行分类,我们把差分电流分解到第二层,用窗口少于一半工频周期的
echies Db5型基小波,考虑到算法,采样速率为
5 kHz,(例如,
Daub
每工频周期100点基于50Hz>。然后,在第二层计算每一个差分电流的能量和标准偏差。我们 可以发现的光谱能量以及标准偏差水平会在涌流保持较高的值。然后 下式计算出来:TIrRGchYzg
I
(7>
,鉴别指数耳可以由
其中,STD是 层次的标准偏差,STD可以有下式确定:
(8>
其中,冋|是」层的n相式的系数, |是它的平均值M是总系数和。那么,在
」层的小波信号的光谱能量可以由 9式计算:
(9>
那么,鉴另持旨数I可就会和阀值叵联系起来。如果三相差分电流的任何一相超过阀 值,继电器就会动作。
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